Details

sample491.0ms

Algorithm

intervals

Results

200.0ms	51×	body	640	valid
102.0ms	56×	body	1280	valid
27.0ms	145×	body	80	valid
12.0ms	25×	body	320	valid
2.0ms	7×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	10	12
1	18	12
2	33	11
3	43	11
4	54	11
5	60	11
6	62	11
done	62	11

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
0.1b	(/ 1.0 (sin B))
0.2b	(/ 1.0 (tan B))
0.3b	(* x (/ 1.0 (tan B)))

rewrite125.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`times-frac`
42×	`add-cube-cbrt` `*-un-lft-identity`
14×	`associate-r`
13×	`add-exp-log` `fma-neg` `prod-diff` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `div-exp` `associate-l`
2×	`tan-quot` `frac-2neg` `associate-*r/` `prod-exp` `clear-num` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `*-commutative` `frac-sub` `flip--`

Counts

4 → 135

Calls

4 calls:

58.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
11.0ms	(/ 1.0 (sin B))
13.0ms	(/ 1.0 (tan B))
30.0ms	(* x (/ 1.0 (tan B)))

series675.0ms

Counts

4 → 12

Calls

4 calls:

349.0ms	(- (/ 1.0 (sin B)) (* x (/ 1.0 (tan B))))
69.0ms	(/ 1.0 (sin B))
79.0ms	(/ 1.0 (tan B))
177.0ms	(* x (/ 1.0 (tan B)))

simplify1.5s

Counts

147 → 147

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	199	1713
1	478	1639
2	1726	1528
done	5001	1459

prune815.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
0.1b	(/ (* x 1.0) (tan B))
0.1b	(/ 1.0 (sin B))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

133×	`times-frac`
107×	`add-sqr-sqrt`
104×	`*-un-lft-identity` `prod-diff`
102×	`add-cube-cbrt`
24×	`div-inv`
14×	`tan-quot` `associate-/r/`
13×	`fma-neg`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`add-log-exp`
4×	`associate-/l*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `prod-exp` `frac-sub` `flip--` `cbrt-unprod` `distribute-lft-out--`

Counts

3 → 188

Calls

3 calls:

74.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
14.0ms	(/ (* x 1.0) (tan B))
7.0ms	(/ 1.0 (sin B))

series373.0ms

Counts

3 → 9

Calls

3 calls:

164.0ms	(- (/ 1.0 (sin B)) (/ (* x 1.0) (tan B)))
171.0ms	(/ (* x 1.0) (tan B))
39.0ms	(/ 1.0 (sin B))

simplify1.9s

Counts

197 → 197

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	284	6281
1	679	5154
2	2696	4197
done	5001	3986

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sin B))
0.1b	(/ 1.0 (sin B))
0.2b	(* (* x (/ 1.0 (sin B))) (cos B))
0.2b	(* x (/ 1.0 (sin B)))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
29×	`add-cube-cbrt` `*-un-lft-identity`
28×	`times-frac`
22×	`add-exp-log` `add-cbrt-cube`
16×	`associate-r`
11×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-/r` `associate-/l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 115

Calls

4 calls:

13.0ms	(/ 1.0 (sin B))
13.0ms	(/ 1.0 (sin B))
72.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
42.0ms	(* x (/ 1.0 (sin B)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1.0 (sin B))
21.0ms	(/ 1.0 (sin B))
139.0ms	(* (* x (/ 1.0 (sin B))) (cos B))
87.0ms	(* x (/ 1.0 (sin B)))

simplify1.4s

Counts

127 → 127

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	140	1194
1	347	1150
2	1633	1022
done	5001	1014

prune733.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (tan B)) (cbrt (tan B)))
0.6b	(cbrt (tan B))
0.6b	(cbrt (tan B))
0.6b	(cbrt (tan B))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
7×	`tan-quot` `cbrt-div`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 87

Calls

4 calls:

29.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
2.0ms	(cbrt (tan B))
2.0ms	(cbrt (tan B))
3.0ms	(cbrt (tan B))

series789.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(* (cbrt (tan B)) (cbrt (tan B)))
169.0ms	(cbrt (tan B))
220.0ms	(cbrt (tan B))
162.0ms	(cbrt (tan B))

simplify6.4s

Counts

99 → 99

Iterations

Useful iterations: done (6.4s)

Iter	Nodes	Cost
0	90	824
1	201	740
2	679	695
3	3865	651
done	5002	648

prune659.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	11	14
done	11	14

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.5s	1655×	body	1280	valid
1.7s	1428×	body	640	valid
951.0ms	5008×	body	80	valid
494.0ms	683×	body	320	valid
177.0ms	337×	body	160	valid